# Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems

arXiv: https://arxiv.org/abs/1609.02356 · HTML: https://mlsanity.com/paper/1609.02356/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2016.

## Built on by (most cited first, 4 of 4)

- [An Adaptive Framework for Learning Unsupervised Depth Completion](https://mlsanity.com/paper/2106.03010/) (2021)
- [Monitored Distillation for Positive Congruent Depth Completion](https://mlsanity.com/paper/2203.16034/) (2022)
- [Adaptive Correspondence Scoring for Unsupervised Medical Image Registration](https://mlsanity.com/paper/2312.00837/) (2023)
- [Composite Optimization Algorithms for Sigmoid Networks](https://mlsanity.com/paper/2303.00589/) (2023)

## Abstract (arXiv)

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are considered as optimal solutions of the energy functionals that mainly consist of data fidelity, regularization and a control parameter for their trade-off. We presents an algorithm to determine the relative weight between data fidelity and regularization based on the residual that measures how well the observation fits the model. Our adaptive regularization scheme is designed to locally control the regularization at each pixel based on the assumption that the diversity of the residual of a given imaging model spatially varies. The energy optimization is presented in the alternating direction method of multipliers (ADMM) framework where the adaptive regularization is iteratively applied along with mathematical analysis of the proposed algorithm. We demonstrate the robustness and effectiveness of our adaptive regularization through experimental results presenting that the qualitative and quantitative evaluation results of each imaging task are superior to the results with a constant regularization scheme. The desired properties, robustness and effectiveness, of the regularization parameter selection in a variational framework for imaging problems are achieved by merely replacing the static regularization parameter with our adaptive one.